Master Polynomials: Conquer Operations, Factoring, and Equations

Question 1

Factor the quadratic trinomial x^2 - 9 using the difference of squares pattern.

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 9)

Answer

(x + 3)(x + 3)

Answer

(x - 9)(x - 9)

Question 2

Which expression is considered a trinomial?

Accepted Answer

x^2 - 3x + 4

Answer

x^2 + 2x

Answer

x^2 + 2x + 3

Answer

2x - 5

Question 3

Solve for x in the equation 2(x - 3) = 8 using algebraic steps.

Accepted Answer

x = 6

Answer

x = 2

Answer

x = 4

Answer

x = 8

Question 4

Factor the polynomial: x^2 - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x - 2)

Answer

(x + 2)

Answer

(x^2 - 4)

Question 5

Find the quotient when dividing the polynomial: 2x^3 - 3x^2 + 5x - 6 by (x - 2)

Accepted Answer

2x^2 - x + 3

Answer

2x^2 + x + 3

Answer

2x^2 - x - 3

Answer

2x^2 + x - 3

Question 6

Identify the term that is NOT present in the polynomial 3x^2 - 5x + 2?

Accepted Answer

x

Answer

3x^2

Answer

-5x

Answer

2

Question 7

Which of the following is NOT a property of polynomials?

Accepted Answer

Polynomials can have complex roots.

Answer

Polynomials can be added and subtracted.

Answer

Polynomials can be multiplied by other polynomials.

Answer

Polynomials can be factored into linear factors.

Question 8

Which graph represents the polynomial y = x^2 - 4?

Accepted Answer

A parabola opening upward

Answer

A parabola opening downward

Answer

A straight line with a positive slope

Answer

A straight line with a negative slope

Question 9

Simplify the expression: (x^2 + 3x + 2) - (x^2 - 2x + 1)

Accepted Answer

5x + 1

Answer

5x + 3

Answer

x + 1

Answer

x + 3

Question 10

Determine the degree of the polynomial: 3x^4 - 2x^2 + 5

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 11

Find a zero of x^2 - 5x + 6

Accepted Answer

3

Answer

2

Answer

4

Answer

5

Question 12

How many terms are in the polynomial 3x³ - 2x² + 5x - 1?

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 13

Factor the polynomial: Express the polynomial as a product of two or more polynomials.

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x - 3)^2

Answer

Cannot be factored

Question 14

Solve the polynomial equation: Find the values of x that make the polynomial equal to zero.

Accepted Answer

x = 2 and x = -2

Answer

x = 2

Answer

x = -2

Answer

x = 1 and x = -1

Question 15

Determine the difference between (3x^3 - 2x^2 + 5x - 1) and (x^3 + 4x^2 - 2x + 3).

Accepted Answer

2x^3 - 6x^2 + 7x + 2

Answer

2x^3 - 6x^2 + 7x - 4

Answer

2x^3 + 6x^2 + 3x - 2

Answer

2x^3 + 6x^2 + 7x - 4

Question 16

If the area of a rectangle is given by the polynomial 2x^2 + 5x - 3 and its length is x + 2, what is its width?

Accepted Answer

2x - 1

Answer

x - 2

Answer

2x + 1

Answer

x + 2

Question 17

Simplify the expression (x^2 - 4) / (x - 2).

Accepted Answer

x - 2

Answer

x + 2

Answer

x^2 + 2x - 4

Answer

x^2 - 2x - 4

Question 18

Determine the degree of the polynomial 3x^5 - 2x^3 + 5x - 1.

Accepted Answer

5

Answer

3

Answer

8

Answer

10

Question 19

Simplify the polynomial: (2x^2 - 5x + 3) - (x^2 + 2x - 1)

Accepted Answer

x^2 - 7x + 2

Answer

x^2 - 3x - 4

Answer

x^2 + 7x + 4

Answer

x^2 + 3x + 2

Question 20

Identify a factor of x^3 + x^2 - 6x:

Accepted Answer

x - 3

Answer

x + 3

Answer

x - 2

Answer

x + 2

Question 21

Identify the leading coefficient of the polynomial 3x^4 - 2x^3 + 5x - 1:

Accepted Answer

3

Answer

1

Answer

5

Answer

-2

Question 22

Solve the polynomial equation x^2 - 5x + 6 = 0.

Accepted Answer

x = 2, 3

Answer

x = -2, -3

Answer

x = 2, -3

Answer

x = -2, 3

Question 23

What is the degree of the polynomial 3x^4 - 2x^2 + 5?

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 24

Find the coefficient of x^3 in the polynomial 2x^5 - 3x^3 + 4x^2 - 1.

Accepted Answer

-3

Answer

2

Answer

0

Answer

4

Question 25

What is the leading term of the polynomial x^4 - 2x^3 + 5x - 7?

Accepted Answer

x^4

Answer

x^3

Answer

5x

Answer

-7

Question 26

Simplify the polynomial: (x³ - 2x² + 4) - (x² - 3x + 2)

Accepted Answer

x³ - 3x² + x + 2

Answer

x³ - x² + 6x - 2

Answer

x³ - 3x² - x + 6

Answer

x³ - x² - 2

Question 27

Factor the polynomial: x² - 4x + 4

Accepted Answer

(x - 2)²

Answer

(x + 2)²

Answer

(x + 4)²

Answer

It cannot be factored.

Question 28

Solve the polynomial equation: x² - 5x + 6 = 0

Accepted Answer

x = 2, x = 3

Answer

x = 1, x = 6

Answer

x = -2, x = -3

Answer

x = -1, x = -6

Question 29

Identify the characteristic that does NOT apply to polynomials:

Accepted Answer

Contain only positive exponents.

Answer

Integers as coefficients.

Answer

Can be graphed as lines or curves.

Answer

Terms combined using operations.

Question 30

Find the degree of the polynomial: 5x⁴ - 2x³ + 7x - 1

Accepted Answer

4

Answer

3

Answer

6

Answer

8

Question 31

What is the leading coefficient of the polynomial 3x³ - 2x² + 5x - 1?

Accepted Answer

3

Answer

1

Answer

5

Answer

-1

Question 32

What is the degree of the polynomial 5x^4 - 2x^3 + x - 7?

Accepted Answer

4

Answer

1

Answer

3

Answer

2

Question 33

Factor the polynomial x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x - 2)(x + 4)

Answer

(x - 4)(x + 2)

Question 34

Find the least common multiple of the polynomials 2x^2 and 3x.

Accepted Answer

6x^2

Answer

3x^2

Answer

6x

Answer

2x

Question 35

Factor the polynomial: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x + 1)

Answer

(x - 3)^2

Answer

(x + 9)(x - 1)

Question 36

What is the degree of the polynomial 3x^4 - 2x^3 + 5x - 1?

Accepted Answer

4

Answer

1

Answer

3

Answer

2

Question 37

Which of the following is the leading coefficient of the polynomial 2x^2 - 3x + 1?

Accepted Answer

2

Answer

3

Answer

-1

Answer

1

Question 38

Is the polynomial x^3 - 2x^2 + x - 2 a monomial, binomial, trinomial, or none of these?

Accepted Answer

Trinomial

Answer

None of these

Answer

Monomial

Answer

Binomial

Question 39

Which expression is a polynomial?

Accepted Answer

3x² + 2x - 1

Answer

√x + 3

Answer

x^(1/2) + 5

Answer

2/x + 4

Question 40

What is the degree of the polynomial 5x³ - 2x + 1?

Accepted Answer

3

Answer

5

Answer

2

Answer

1

Question 41

Simplify the expression: (2x² + 3x - 1) + (x² - 5x + 2)

Accepted Answer

3x² - 2x + 1

Answer

x² - 2x + 1

Answer

3x² + 8x + 1

Answer

3x² - 8x + 1

Question 42

Subtract (x² - 4x + 3) from (2x² + 5x - 1).

Accepted Answer

x² + 9x - 4

Answer

3x² + x - 2

Answer

x² - x + 2

Answer

x² + x + 2

Question 43

What is the product of (x + 2) and (x - 3)?

Accepted Answer

x² - x - 6

Answer

x² + 5x - 6

Answer

x² - 5x - 6

Answer

x² + x - 6

Question 44

Factor the polynomial x² - 9.

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 3)(x + 3)

Answer

(x + 9)(x - 9)

Answer

(x - 3)(x - 3)

Question 45

What are the solutions to the equation x² - 4x + 3 = 0?

Accepted Answer

x = 1, x = 3

Answer

x = 1, x = -3

Answer

x = -1, x = 3

Answer

x = -1, x = -3

Question 46

What is the value of 2x³ - 5x + 1 when x = 2?

Accepted Answer

9

Answer

-9

Answer

1

Answer

-1

Question 47

Simplify the following polynomial expression: (4x² - 5x + 2) + (2x² + 3x - 1)

Accepted Answer

6x² - 2x + 1

Answer

2x² - 8x + 3

Answer

6x² + 8x + 1

Answer

2x² + 2x - 1

Question 48

What is the remainder when x³ - 2x² + 5x - 3 is divided by (x - 2)?

Accepted Answer

7

Answer

0

Answer

5

Answer

-3

Question 49

Factor the polynomial completely: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 3)²

Answer

x(x - 9)

Answer

(x - 3)²

Question 50

A rectangular garden has a length of (x + 5) feet and a width of (x - 2) feet. What is the area of the garden in square feet?

Accepted Answer

x² + 3x - 10

Answer

2x + 3

Answer

4x + 6

Answer

x² - 10

Question 51

Which of the following is NOT a polynomial?

Accepted Answer

3 / (x + 1)

Answer

5x³ - 2x² + x - 7

Answer

8

Answer

x² - 4